A322858 List of e-perfect numbers that are not e-unitary perfect.

17424, 87120, 121968, 226512, 296208, 331056, 400752, 505296, 540144, 609840, 644688, 714384, 749232, 818928, 923472, 1028016, 1062864, 1132560, 1167408, 1237104, 1271952, 1306800, 1376496, 1446192, 1481040, 1550736, 1585584, 1655280, 1690128, 1759824

Offset

1,1

Comments

The e-unitary perfect numbers are numbers k such that the sum of their exponential unitary divisors (A322857) equals 2k. Apparently most of the e-perfect numbers (A054979) are also e-unitary perfect numbers: the first 150 e-perfect numbers are also the first 150 e-unitary perfect numbers. But A054979(151) = 17424 is not e-unitary perfect.

Minculete and Tóth ask if there is any e-unitary perfect number which is not e-perfect.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp., Vol. 35 (2011), pp. 205-216.

Mathematica

f[p_, e_] := DivisorSum[e, p^# &]; esigma[n_] := Times @@ f @@@ FactorInteger[n]; ePerfectQ[n_] := esigma[n] == 2n; fu[p_, e_] := DivisorSum[e, p^# &, GCD[#, e/#]==1 &]; eusigma[n_] := Times @@ fu @@@ FactorInteger[n]; euPerfectQ[n_] := eusigma[n] == 2n; aQ[n_] := ePerfectQ[n] && !euPerfectQ[n]; Select[Range[125000], aQ]

Crossrefs

Cf. A051377, A054979, A322857.

Sequence in context: A219325 A255780 A023942 * A251465 A278004 A031640

Adjacent sequences: A322855 A322856 A322857 * A322859 A322860 A322861

Keyword

nonn

Author

Amiram Eldar, Dec 29 2018

Status

approved